Since his invention (Patent Document 1) by C. W. Musser, the founder, wave gear devices have been the subject of a variety of inventions and designs until the present day, both by him and other researchers including the inventor of the present invention. Even with regards specifically to tooth profile, the inventions are diverse. For example, the inventor of the present invention has proposed using an involute tooth profile as the basic tooth profile in Patent document 2; and proposed a method for designing a tooth profile, where a technique is used in which meshing of a rigid internally toothed gear and a flexible externally toothed gear is approximated as a rack in order to obtain an addendum tooth profile for the two gears that contact each other over a wide range, in Patent Documents 3 and 4.
Typically, a wave gear device has an annular rigid internally toothed gear; a flexible externally toothed gear arranged coaxially on an inside of the rigid internally toothed gear; and a wave generator fitted on an inside of the flexible externally toothed gear. The flexible externally toothed gear comprises a flexible cylindrical barrel part; a diaphragm extending in a radial direction from a rear end of the cylindrical barrel part; and an external tooth formed on an outer circumferential surface portion on a side towards a front-end opening of the cylindrical barrel part. The flexible externally toothed gear is deflected into an ellipsoidal shape by the wave generator, and caused to mesh with the rigid internally toothed gear at both end parts in the direction of the major axis of the ellipse.
The amount of deflection of the external teeth of the flexible externally toothed gear deflected into an ellipsoidal shape increases from a side towards the diaphragm to the front-end opening along the tooth trace direction of the external teeth, the amount of deflection being substantially proportional with respect to the distance from the diaphragm. Each portion of the teeth part of the flexible externally toothed gear is repeatedly deflected in the radial direction as the wave generator rotates. However, up to the present, insufficient consideration has been given with regards to a method for setting a rational tooth profile, in which the deflecting movement (coning) of the flexible externally toothed gear caused by the wave generator has been taken into account.
In Patent Document 5, the inventor of the present invention has proposed a wave gear device provided with a tooth profile in which the coning of the tooth has been taken into account. In the wave gear device proposed in Patent document 5, an arbitrary position of a cross section perpendicular to the axis of the flexible externally toothed gear, which is taken on an arbitrary position along the tooth trace direction, is designated as a main cross-section. A configuration is in place so that the degree of deflection 2 κmn (where κ is a deflection factor, m is the module, and n is a positive integer) of the flexible externally toothed gear from a neutral circle of the rim before deflection is set so that the rim is deflected to a zero-deviation state of 2 κmn (k=1) at a major-axis position on a neutral line of the elliptical rim of the gear in the main cross-section.
The meshing between the flexible externally toothed gear and the rigid internally toothed gear is approximated as rack meshing. A movement trajectory of a tooth of the flexible externally toothed gear relative to a tooth of the rigid internally toothed gear that accompanies rotation of the wave generator is determined for an axially perpendicular cross-section at each position, including the main cross-section, along the flexible externally toothed gear in the tooth trace direction. There is determined a first similarity curve BC, in which a curve portion extending from a top point A to a next bottom point B of a zero-deviation movement trajectory obtained on the main cross-section is scaled down λ-fold (where λ<1) using the point B as the center of similarity transformation. The first similarity curve BC is used as a basic tooth profile of the addendum of the rigid internally toothed gear.
Then, there is determined a second similarity curve in which a curve obtained by rotating the first similarity curve BC by 180 degrees about an end point C of the first similarity curve BC is scaled up (1−λ)/λ-fold using the point C as the center of similarity transformation. The second similarity curve is used as a basic tooth profile of the addendum of the flexible externally toothed gear.
In addition, the tooth profile of the flexible externally toothed gear has been subjected to profile shifting, applied to tooth profile portions on both sides of the main cross-section in the direction of the tooth trace of the flexible externally toothed gear, so that both of each negative-deviation-side movement trajectory and each positive-deviation-side movement trajectory describe a curve that comes into contact at a bottom part of the zero-deviation movement trajectory; the negative-deviation-side movement trajectory being obtained in each axially perpendicular cross-section that is deflected to a negative deviation state (deflection factor κ<1) in which deflection occurs further towards the diaphragm than the main cross-section; and the positive-deviation-side movement trajectory being obtained in each axially perpendicular cross-section that is deflected to a positive deviation state (deflection factor κ>1) in which deflection occurs further towards the front-end opening than the main cross-section.
In a wave gear device in which the tooth profile has been formed as described above, it is possible to obtain effective meshing over the entire range of the tooth trace extending from the main cross-section to the side towards the diaphragm and the range of the tooth trace extending from the main cross-section to the opening part, centered around continuous meshing of the tooth profile extending over a wide range on the main cross-section. It is thereby possible to transmit a larger torque compared to a conventional wave gear device in which meshing occurs over a narrower tooth trace range.